India does not tax it, and Switzerland mostly does not either
The Indian side is straightforward: India has no inheritance tax and no gift tax, and the income-tax law exempts anything you receive under a will, by inheritance, or as a gift from a relative, under the proviso to Section 56(2)(x), so the Indian receipt is tax-free. Switzerland is more favourable than most people assume, and for a structural reason worth understanding. There is no federal inheritance or gift tax in Switzerland. It is charged by the individual cantons, and the cantons vary, but two features work in your favour.
First, on relationships: a surviving spouse or registered partner is exempt from inheritance tax in every canton, and direct descendants, your children, are exempt in most cantons, with only a few still taxing them. So a close-family inheritance often bears little or no Swiss tax to begin with. The second feature is the one that really matters for an inheritance coming from India, and it is about where the tax attaches.
Swiss tax follows the deceased's home, not yours
This is the key point. Swiss cantonal inheritance tax on movable assets, money, investments, and the like, attaches to the last home, the domicile, of the person who died, not to where you as the heir live. So if your parent lived and died in India, the movable part of their Indian estate is generally outside Swiss cantonal inheritance tax altogether, even though you are resident in Switzerland. Your being a Swiss resident does not pull the Indian movable estate into the Swiss net, because the deceased's Indian domicile, not your Swiss residence, sets the nexus. For immovable property, the rule is that it is taxed where it sits, so an Indian flat or house is a matter for India, which has no death tax.
The practical result is that an inheritance from an India-based parent is, in most cases, largely or entirely outside Swiss inheritance tax, a distinctly favourable position compared with Germany, Ireland or France, where your residence alone can pull the Indian estate into charge. The exception to keep in mind is if the deceased had themselves been resident in Switzerland, which changes the analysis, or if you are in one of the few cantons that tax children, but for a classic case of inheriting from family in India, Switzerland's reach is limited. There is no Switzerland-India inheritance treaty, and none is needed because the Indian estate falls outside the Swiss net anyway. Our role is the Indian end: the legal heir paperwork, a valuation of the Indian asset, a certificate confirming no Indian death tax, and repatriation of the inherited funds to you.